So, here's a houserule I've been playing with for decades now that I apparently forgot was a house rule. My groups have found it fun, I figure some other people might. If there are any questions about specifics that need clarification, just ask.
Initiative Homebrew Modification
As per usual, initiative order is checked at the start of the combat after the surprise round. Additionally, one can hold & ready actions to change where they're going in the initiative as per usual. The primary change lies in that things which disrupt Initiative Count specifically can be used to change an enemy's initiative count.
That is to say, one can use, say, Unprepared Combatant to drop that initiative 27 Lich down to Initiative 23, letting your two buddies go ahead of him rather than getting death ray'd in the face.
One can also increase an initiative count, but again, only things that increase initiative specifically qualify.
Some caveats, of course.
1) A character can never go twice in the same round via this. As in, Init 27 Lich goes, then gets dropped to 23, cannot go again.
2) If a character's initiative is increased in combat, that does not enable them in any way shape or form to retroactively apply their turn's actions as occurring BEFORE the newly lower-than-their-initiative-count characters.
3) In effect, all changes to initiative only take effect in the next round of combat.
4) You can 'reshuffle' as a move action instead of holding or readying an action to change your initiative number. You roll your initiative again to find your new place in the turn order. You must take the new roll, even if it's worse.
5) Penalties and bonuses to initiative (whether count or roll) apply on reshuffles. For instance, if you are still affected by Unprepared Combatant's 1 min/level duration, all reshuffling you do will still apply the -4.
6) You cannot combine a reshuffle, a readied action, or a held action in the same round. Just because you don't like your reshuffle result, doesn't mean you get to cheat it this round.
7) Bonuses and penalties to dexterity do not affect your initiative count in turn order. They will, however, effect your reshuffle rolls.
I'm not all here right now, a little ill actually, but I believe that's pretty much everything. If anything's unclear I'll happily clarify as best as I can.
I think this would encourage metagaming. Initiative is an abstraction that establishes the relative order of turns between combat participants. It doesn't make sense that players could manipulate initiative order in this manner. A character has no knowledge that their opponent goes at an initiative count of 27. They only know that player A goes before monster X (and only after the first round of combat has taken place).
A better way to handle this would be to roll initiative each round. Which is still problematic, as it prolongs dealing with the combat round and creates unbalanced situations where a creature acts twice before its opponent's turn (a case that isn't covered by your rules).